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\section{Conclusion}
\label{sec:conclusion}
In this report, we have presented a technique to implement a collaborative filtering 
algorithm using $k$-rank of approximation, regularization and learning rate on the MovieLens 100k
Rating Dataset. We explain how to reduce the computation time with an
approximation to reduce the total error by using stochastic gradient descent.
We explain how adding residual fitting improves the model and reduces error and
we demonstrate how to tune all of our parameters to reduce MSE and show the
effects on MAE.

